非线性恢复力耦合的振动系统广义同步与参数识别

对于一类非线性恢复力无法精确解析表达的简谐激励振动系统，建立了由原系统非线性恢复力激振的派生系统.证明了派生系统与原系统可以达到广义同步.派生系统可以自动与激励力频率、大小变化的原非线性振动系统保持广义同步.证明了由派生系统的广义同步，可以识别出原系统的阻尼系数、激振力幅值与频率.由Duffing系统的仿真计算结果可以看出，这种方法是有效的，而且识别精度较高. 关键词： 非线性恢复力 广义同步 混沌

Generalized synchronization by coupling of restoring force and determination of parameters in vibration systems

For a class of vibration systems excited by external harmonic force，generally the restoring force cannot be given an accurate analytical expression. For such system, a derived system of generalized synchronization (GS) is set up. The GS between the two systems is proved. Since there is no time element in the equations of the derived system，the derived system can reach GS with the original system automatically，even if the frequency and amplitude of external force are varied. By using GS，a novel method to determine parameters in a vibration system，e.g.，the damping coefficient and the amplitude and frequency of external exciting force，is presented and proved. From the simulation of Duffing system，it can be seen that the presented method is effective and can give a result of high accuracy.